CN111856945A - Lower limb exoskeleton sliding mode control method based on periodic event trigger mechanism - Google Patents

Lower limb exoskeleton sliding mode control method based on periodic event trigger mechanism Download PDF

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CN111856945A
CN111856945A CN202010783390.XA CN202010783390A CN111856945A CN 111856945 A CN111856945 A CN 111856945A CN 202010783390 A CN202010783390 A CN 202010783390A CN 111856945 A CN111856945 A CN 111856945A
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sliding mode
lower limb
exoskeleton
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CN111856945B (en
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王婕
刘佳浩
张高巍
李荣利
孙建军
杨鹏
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Hebei University of Technology
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Abstract

The invention discloses a lower limb exoskeleton sliding mode control method based on a periodic event trigger mechanism, which comprises the following steps of: 1) establishing a lower limb exoskeleton system dynamic model according to a Lagrange equation, and deducing a state space expression and a system comprehensive state vector expression; 2) acquiring lower limb movement data of a healthy human body by using a sensor, and acquiring an expected track of a lower limb exoskeleton joint through function fitting, specifically acquiring an angle expected track, an angular velocity expected track and an angular acceleration expected track; obtaining a system comprehensive state vector by combining the expected track, the actual operation angle and the angular speed, and calculating a system measurement error according to the system comprehensive state vector of the previous event triggering time and the current sampling time; 3) presetting a threshold value and a sampling period of a measurement error, and designing a sliding mode controller based on a period event trigger mechanism for controlling a lower limb exoskeleton system according to the threshold value and the sampling period of the measurement error; the method can ensure the gradual stability of the lower limb exoskeleton system, saves communication resources and unnecessary hardware cost, reduces the abrasion of actuators and parts, and has engineering application value.

Description

Lower limb exoskeleton sliding mode control method based on periodic event trigger mechanism
Technical Field
The invention relates to the technical field of lower limb exoskeleton robot control, in particular to a lower limb exoskeleton sliding mode control method based on a periodic event trigger mechanism.
Technical Field
In recent years, control methods for lower extremity exoskeletons have become a hot issue of research. Because the exoskeleton system is a multi-input multi-output system with uncertainty and external interference, the stability and robustness of the system are difficult to ensure by classical linear control methods such as PID control and the like. Some robust control methods, such as adaptive control, fuzzy control, sliding mode control and the like, can ensure the robust stability of the system in exoskeleton control, wherein the sliding mode control is widely concerned due to strong robustness and anti-interference capability. In practical application, the lower limb exoskeleton control needs a digital sensor to acquire various state information such as angles, angular speeds and pressures in real time to calculate control torque, and control signals are periodically updated under a given step length. When the state information of the system does not change significantly, the control signal is updated meaninglessly. Therefore, an event-triggered control method has been widely studied, which updates the control signal only when the state information satisfies a certain condition, so that the processor resource utilization rate of the controller is higher and the number of changes of the state of the actuator is reduced in practical applications. For example, patent CN110989348A discloses an aircraft sliding mode control method based on an event trigger mechanism, which uses sliding mode control to ensure the stability of the system and have certain robustness to system parameters and external interference signal changes, and introduces an event trigger mechanism to reduce data transmission and save communication resources. However, in most of the studies on event-triggered control, the event-triggered mechanism is implemented based on continuous status monitoring, so that it is necessary to provide sensors and related circuits for continuous status monitoring, and the hardware cost of communication resources and real-time monitoring system status is high.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a lower limb exoskeleton sliding mode control method based on a periodic event trigger mechanism. The method solves the problem of high-precision tracking control of the lower limb exoskeleton under the conditions of external interference and limited communication resources, saves the hardware cost of communication resources and monitoring the system state in real time on the premise of ensuring the robustness and stability of the system, and reduces the abrasion of an actuator.
The invention provides a technical scheme for solving the technical problem, and designs a lower limb exoskeleton sliding mode control method based on a periodic event trigger mechanism, which is characterized by comprising the following operation steps:
step 1: establishing a lower limb exoskeleton system dynamic model according to a Lagrange equation, and deducing a state space expression and a system comprehensive state vector expression;
step 2: acquiring lower limb movement data of a healthy human body by using a sensor, and acquiring an expected track of a lower limb exoskeleton joint through function fitting, specifically acquiring an angle expected track, an angular velocity expected track and an angular acceleration expected track; obtaining a system comprehensive state vector by combining the expected track, the actual operation angle and the angular speed, and calculating a system measurement error according to the system comprehensive state vector of the previous event triggering time and the current sampling time;
and step 3: presetting a threshold value and a sampling period of a measurement error, and designing a sliding mode controller based on a period event trigger mechanism for controlling a lower limb exoskeleton system according to the threshold value and the sampling period of the measurement error;
and 4, step 4: the Lyapunov theory is utilized to prove that the designed sliding mode controller based on the periodic event trigger mechanism can ensure the asymptotic stability of the lower limb exoskeleton system;
and 5: and (3) establishing a Matlab/Simulink simulation system under sliding mode control of the lower extremity exoskeleton system under a periodic event trigger mechanism for simulation, analyzing a simulation result and verifying the effectiveness of the method provided by the invention.
Compared with the prior art, the invention has the beneficial effects that:
(1) compared with the common periodic sampling control in practical application, the sliding mode control method based on the periodic event trigger mechanism determines whether to calculate and update the control law by judging whether the system state meets the preset condition or not in each sampling, thereby avoiding the calculation and update of the control law in each sampling period and the frequent action of an actuator, effectively saving the calculated amount and communication resources, reducing the part abrasion and prolonging the service life of the actuator.
(2) Compared with continuous event trigger control, the method reduces unnecessary hardware cost for continuously monitoring the system state, only needs a common digital sensor to measure the system state in each sampling period, and has more practicability in the aspect of engineering application. Meanwhile, the robustness and the anti-interference capability of the system are improved by combining a sliding mode control method. The method of the invention saves hardware cost and system resources on the premise of ensuring the asymptotic stability of the system.
Drawings
Fig. 1 is a schematic diagram of a lower extremity exoskeleton system, labeled: 1 is a pneumatic muscle connection point, 2 is a mass center, 3 is a joint, 4 is a pneumatic muscle, and theta1And theta2The angles of the hip joint and the knee joint, respectively.
Fig. 2(a) shows a desired trajectory of the hip joint angle of the lower extremity exoskeleton and fig. 2(b) shows a desired trajectory of the knee joint angle.
Fig. 3 is a structural diagram of a sliding mode controller based on a periodic event trigger mechanism according to an embodiment of the method of the present invention, in which the sliding mode control law is equation (9) and the trigger condition is equation (11).
Fig. 4 is a design flowchart of a sliding mode controller based on a periodic event trigger mechanism according to an embodiment of the method of the present invention.
Fig. 5(a) is a graph showing the tracking effect of the hip joint and the knee joint by the simulation of the method of the present invention, fig. 5(b) is a graph showing the tracking effect of the hip joint and the knee joint by the simulation of the method of the present invention, and fig. 5(c) is a graph showing the variation of the two norms of the sliding mode surface s by the simulation of the method of the present invention with time.
Fig. 6(a) is a graph of the control input torque of the hip joint simulated by the method of the present invention, and fig. 6(b) is a graph of the control input torque of the knee joint simulated by the method of the present invention.
FIG. 7 is a scatter diagram of event intervals under a periodic event trigger mechanism obtained by simulation using the method of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention.
The invention provides a lower limb exoskeleton sliding mode control method (a method for short) based on a periodic event trigger mechanism, which is characterized by comprising the following operation steps:
step 1: establishing a lower limb exoskeleton system dynamic model according to a Lagrange equation, and deducing a state space expression and a system comprehensive state vector expression;
step 2: acquiring lower limb movement data of a healthy human body by using a sensor, and acquiring an expected track of a lower limb exoskeleton joint through function fitting, specifically acquiring an angle expected track, an angular velocity expected track and an angular acceleration expected track; obtaining a system comprehensive state vector by combining the expected track, the actual operation angle and the angular speed, and calculating a system measurement error according to the system comprehensive state vector of the previous event triggering time and the current sampling time;
and step 3: presetting a threshold value and a sampling period of a measurement error, and designing a sliding mode controller based on a period event trigger mechanism for controlling a lower limb exoskeleton system according to the threshold value and the sampling period of the measurement error;
and 4, step 4: the Lyapunov theory is utilized to prove that the designed sliding mode controller based on the periodic event trigger mechanism can ensure the asymptotic stability of the lower limb exoskeleton system;
and 5: and (3) establishing a Matlab/Simulink simulation system under sliding mode control of the lower extremity exoskeleton system under a periodic event trigger mechanism for simulation, analyzing a simulation result and verifying the effectiveness of the method provided by the invention.
The dynamic equation of the lower limb exoskeleton system (system for short) in the step 1 is as follows:
Figure BDA0002621013480000051
f (theta) < alpha >, < alpha > and,
Figure BDA0002621013480000052
G (theta) is respectively abbreviated as F, H, G, and the obtained product is obtained by arranging:
Figure BDA0002621013480000053
wherein θ ═ θ1,θ2]TIs a lower extremity exoskeleton joint angle vector, and θ1And theta2The angles of the hip joint and the knee joint respectively;
Figure BDA0002621013480000054
and
Figure BDA0002621013480000055
respectively representing the joint angular velocity and angular acceleration vectors of the lower extremity exoskeleton. F (theta) belongs to R2×2A generalized inertia matrix;
Figure BDA0002621013480000056
is a matrix of centrifugal and coriolis forces; g (theta) ∈ R2And represents a gravity vector. τ ═ τ [ τ ]1,τ2]TRepresents a control moment vector, and1and τ2Respectively represent the control moment of the lower limb exoskeleton hip joint and the knee joint driver. Tau ish＝[τh1,τh2]TRepresents the wearer joint moment vector, and τh1And τh2Respectively representing the control moment of the hip joint and the knee joint of the human body. d ═ F-1τhRepresenting the system interference vector.
The state space expression obtained according to equation (2) is:
Figure BDA0002621013480000057
the simplified state space expression is:
Figure BDA0002621013480000058
wherein,
Figure BDA0002621013480000059
represents a tracking error, and e1And e2Respectively, exoskeleton hip joint and knee joint trajectory tracking errors. ThetadThe desired trajectory for the lower extremity exoskeleton joint angles,
Figure BDA00026210134800000510
the desired trajectory for the angular velocity is,
Figure BDA00026210134800000511
an expected trajectory for the angular acceleration vector; vector quantity
Figure BDA00026210134800000512
In order to synthesize the state vector for the system,
Figure BDA00026210134800000513
the angle expected track and the angular speed expected track of the lower extremity exoskeleton joint are thetad＝[θd1,θd2]T、
Figure BDA00026210134800000514
Having the formula:
Figure BDA0002621013480000061
the method for acquiring the desired angle track and the desired angular speed track of the lower extremity exoskeleton joint comprises the following steps: the relevant data of the healthy human body in the walking process is measured through an angular displacement sensor, and a four-order Fourier curve is formed through fitting of a curve fitting tool box in Matlab, and is shown in an attached figure 2. Obtaining the constant a in the formula (5)l,j、bl,jTo obtain the desired trajectory of the angle and the desired trajectory of the angular velocity of the exoskeleton joint of the lower limb, and further to obtain the desired trajectory of the angular acceleration. a isl,0For the lower extremity exoskeleton angle desired value, omega, at the initial momentlIs a fourier series frequency. By choosing an appropriate constant c0、c1、c2、c3> 0 such that thetad||≤c0，
Figure BDA0002621013480000062
At each sampling moment, calculating the comprehensive state variable of the system according to the angle expected track, the angular speed expected track and the angular acceleration expected track of the lower extremity exoskeleton joint and the corresponding actual running numerical value
Figure BDA0002621013480000063
And combining the system comprehensive state variable eta (t) at the moment of triggering the last eventi) So as to obtain the measurement error value of the lower limb exoskeleton system
Figure BDA0002621013480000064
The specific implementation manner of the sliding mode controller based on the periodic event triggering mechanism in the step 3 is as follows: presetting a threshold value and a sampling period of a measurement error, and designing a sliding mode control law; calculating a comprehensive state vector of the system at each sampling moment, calculating a measurement error, and defining the condition that the measurement error reaches or exceeds a preset measurement error threshold value as an event; when an event occurs, the sliding mode controller is triggered to calculate and update the control law, the zero-order retainer ZOH is used for keeping the control law until the next event triggering moment, and then the actuator is used for regulating and controlling the running state of the lower limb exoskeleton; the event is monitored through continuous periodic sampling, and when the event occurs, the sliding mode controller regulates and controls the lower limb exoskeleton system, so that the measurement error is smaller than a preset measurement error threshold value, namely the running state of the lower limb exoskeleton system tends to or reaches a preset ideal state. The sliding mode controller is shown in figure 3. The sliding mode controller under the periodic event trigger mechanism not only saves communication resources on the basis of realizing system tracking performance, but also needs to monitor the system state in real time unlike a continuous event trigger mechanism, and only needs to monitor the system state at each sampling period time under the periodic event trigger mechanism, thereby saving the hardware cost for continuously monitoring the system state.
The design process of the sliding mode controller based on the periodic event trigger mechanism in the step 3 is as follows:
designing a sliding mode surface based on a track tracking error as follows:
s＝Λe1+e2(6)
in the formula, lambda is ═ diag [ lambda ]1,λ2]，λ1,λ2＞0。
The Lyapunov function was designed as:
Figure BDA0002621013480000071
deriving V yields:
Figure BDA0002621013480000072
the sliding mode controller and the periodic event triggering conditions are designed as follows:
Figure BDA0002621013480000073
K＞0,K1＞d0+(1+)α (10)
Figure BDA0002621013480000074
Figure BDA0002621013480000075
wherein the time t ∈ [ t ]i,ti+1) And t isiRepresents the moment of occurrence of the ith event of the system and is a function of the vector η. Sign(s) ═ signs1,signs2]TExpression symbolA vector of sign functions. h denotes the sampling period of the system. Measurement error
Figure BDA0002621013480000076
Where t e [ t ∈ [ [ t ]i,ti+1). The constant satisfies 0 < 1 and the constant alpha > 0. Constant beta is | | F-1Upper bound of |, LiFor a function phi in a set phiiLipschitz constant of, here
Figure BDA0002621013480000077
According to the Lipschitz condition, when eta + e, eta belongs to phiiTime of flight
Figure BDA0002621013480000081
For the system to be stable, the control gain K is set to any normal number, and the gain K is switched1＞d0+(1+)α，d0Is the upper bound of system disturbances, being any normal number. At time t e [ t ∈i,ti+1) In that the sampling period h is less than
Figure BDA0002621013480000082
m＝[K+(λmax+λmin)(λmax+1)/λmin]w+d0+c1+c2+c3，λmin、λmaxRespectively, the minimum and maximum eigenvalues of matrix Λ, w is greater than or equal to the norm of the initial sliding-mode surface | | s (0) | |.
Substituting the control law formula (9) into the formula (8), when t is the same as [ t ]i,ti+1) Then, obtaining:
Figure BDA0002621013480000083
when η + e, η ∈ Φ, obtained by combining formula (14) and formula (15)iTime of flight
Figure BDA0002621013480000084
The specific process of the step 4 is as follows: the stability of the sliding mode controller based on the periodic event trigger mechanism, which is designed in the step 3, is verified by analyzing the stability problem of the system in different sampling periods, and the stability is specifically divided into the following conditions:
1) when the limit case sampling period h is equal to 0, the constant is equal to 0 and the gain K is switched1＞d0+ α, conditional expression (11) is equivalent to a continuous event triggered condition. Firstly, the method of inversing the syndrome proves when t is an element of ti,ti+1) Time, eta + e, eta e phiiThe situation is always established; by definition can be obtained
Figure BDA0002621013480000085
Let eta ∈ phiiAt t ∈ [ t ]i,ti+1) The time is not always true, and the existence time can be known due to the continuity of s
Figure BDA0002621013480000086
Satisfy the requirement of
Figure BDA0002621013480000087
And is
Figure BDA0002621013480000088
However, when
Figure BDA0002621013480000089
Time of flight
Figure BDA00026210134800000810
Still, it is possible, as can be seen by the trigger condition,
Figure BDA00026210134800000811
in combination with formula (14) to
Figure BDA00026210134800000812
Namely, it is
Figure BDA00026210134800000813
Which contradicts the hypothesis. It is therefore concluded that,
Figure BDA00026210134800000814
and does not exist, i.e. at t e [ t ]i,ti+1) Time eta e phiiThis is always true. In combination with formula (16), yields:
Figure BDA0002621013480000091
from the above equation, the slip-form surface s is consistently bounded and limited
Figure BDA0002621013480000092
Is present.
Integrating the two sides of the inequality (17) to obtain:
Figure BDA0002621013480000093
the above formula is combined with the Barbalt theorem to obtain
Figure BDA0002621013480000094
Namely, it is
Figure BDA0002621013480000095
The system is therefore asymptotically stable.
According to the definition, e can be obtained2＝-Λe1+ s, so the system can be written as:
Figure BDA0002621013480000096
considering the Lyapunov function
Figure BDA0002621013480000097
And deriving it to yield:
Figure BDA0002621013480000098
according to the consistency and the boundedness of s, the | | | s | ≦ s (0) | | | w is obtained by combining the formula (18):
Figure BDA0002621013480000099
according to the above formula, if | | | e1||＞w/λminThen, then
Figure BDA00026210134800000910
If true, further get | | | e1||≤w/λmin. According to the nature of the triangle inequality, | | e2||≤λmax||e1||+||s||≤λmaxw/λmin+w。
Combined triangle inequality pair
Figure BDA00026210134800000911
Taking the derivative, one can obtain:
Figure BDA00026210134800000912
2) when the sampling period h is greater than 0, the constant is greater than 0 and the gain K is switched1＞d0+ (1+) α. Events can only be monitored at the sampling time. So when t e [ t ]i,ti+1) Time inequality
Figure BDA00026210134800000913
Cannot be guaranteed to be constant. However, when the sampling period h is close to 0, when h is small enough, there is a constant
Figure BDA0002621013480000101
And is
Figure BDA0002621013480000102
So that
Figure BDA0002621013480000103
The method obtains the current t epsilon [ t ] by using a back-syndrome method in the same wayi,ti+1) Time, eta + e, eta e phiiIf this is true, equation (17) can still be obtained by combining equation (16), and the system asymptotic stability is further obtained.
The specific process set by the sampling period h is as follows: according to the process of analyzing the stability problem of the system in different sampling periods, t is the ∈ [ t ∈ [ [ t ]i,ti+1) There is a sufficiently small normal number h*H is less than or equal to h*Time inequality
Figure BDA0002621013480000104
And (4) meeting the requirement. According to the above description, if the error is measured
Figure BDA0002621013480000105
Satisfy inequality
Figure BDA0002621013480000106
The system asymptotically stabilizes. Similar to the derivation of equation (22), further we can derive:
Figure BDA0002621013480000107
consider the following two cases:
1) if the event trigger condition (11) happens to be satisfied at the sampling time, the events are triggered synchronously and for t e [ t ∈ [ [ t ]i,ti+1)，
Figure BDA0002621013480000108
2) If the event trigger condition (11) is satisfied before the sample arrives, i.e.
Figure BDA0002621013480000109
Figure BDA00026210134800001010
When the conditional expression (11) is satisfied, the event is at ti+1＝ti+kiAnd h, triggering. For the
Figure BDA00026210134800001011
Integration on both sides of the differential inequality (23) can be derived (initial conditions)
Figure BDA00026210134800001012
Figure BDA00026210134800001013
The arrangement (24) gives:
Figure BDA00026210134800001014
to ensure
Figure BDA00026210134800001015
Design parameters
Figure BDA00026210134800001016
When h is less than or equal to h*Xi (h)*)＜(1+)α/(βLi)。
In summary, when the sliding mode control laws (9) - (10) based on the periodic event trigger conditional expressions (11) - (12) are applied to the lower extremity exoskeleton system (5), the system asymptotically stabilizes.
The Matlab/Simulink simulation system in the step 5 consists of a system expected track (formula (5)), a periodic event trigger (formula (11)), a sliding mode controller (formula (9)) and a lower limb exoskeleton model (formula (5)), and the system expected track and the actual track of the lower limb exoskeleton model changing along with time are combined to calculate a system measurement error; and inputting the measurement error into a periodic event trigger to generate a trigger time, and inputting the trigger time into a sliding mode controller to obtain a sliding mode control law and inputting the trigger time into a lower limb exoskeleton model for regulation and control to form closed-loop feedback.
The simulation process comprises the following specific steps:
(1) parameter setting
Setting parameters of the lower limb exoskeleton hip joint and knee joint expected trajectory formula (3):
a1,0＝0.3315，[a1,1a1,2a1,3a1,4]＝[0.0733-0.08063-0.006612-0.003744]，ω1＝5.545，[b1,1b1,2b1,3b1,4]＝[-0.09017-0.004430.01522-0.007166]；a2,0＝0.6452，[a2,1a2, 2a2,3a2,4]＝[-0.1497-0.2607-0.04603-0.0005026]，ω2＝5.859，[b2,1b2,2b2,3b2,4]＝[-0.3618-0.011920.039920.0005958]。
setting parameters of a periodic event trigger:
the parameter in formula (10) is set to 2.125. In formula (11), the parameter is set to 0.8, and α is set to 4. Upper limit parameter h of sampling period of periodic event trigger mechanism*Fig. 5-7 show simulation results for a sampling period h of 0.001 seconds, when the period h is 0.0024 seconds.
The parameters of the sliding mode controller are set as follows:
the matrix Λ ═ diag [8,4 ] in formula (6)]In the formula (9), the control gain K is 100, K1＝12。
And (3) setting other parameters:
the initial tracking error of the lower extremity exoskeleton system formula (3) is e (0) ═ 0.1,0.2, -0.2,0.3]TThe parameter β is set to 5, and for i 1,2i2. The system disturbance is set to d ═ 2sin (2t),2cos (2t)]T，d 02. Parameter c1＝0.7427，c2＝0.8101，c31.7741. The simulation time was set to 1.1 seconds and the simulation step size was set to 0.000001 seconds.
The results of simulation verification of the proposed method of the present invention with the above given parameters are shown in fig. 5-7 and table 1. The control effect of the sliding mode control algorithm based on the periodic event triggering applied to the lower limb exoskeleton is shown in fig. 5. As can be seen from fig. 5(a) and 5(b), the hip and knee joint angles and angular velocities can both track the desired trajectory quickly and accurately. From fig. 5(c), it can be seen that the slip-form surface rapidly tends to within 2% error band in a short time and tends to converge. As can be seen from fig. 6-7, the effect of discontinuous aperiodic control under the periodic event trigger mechanism is shown.
TABLE 1 number of triggers under different sampling periods and trigger regimes
Figure BDA0002621013480000121
In table 1, the conventional periodic sampling mechanism refers to that the system samples the system state and calculates and updates the controller at each fixed periodic time. The periodic event triggering mechanism provided by the invention samples the system state at each fixed periodic moment, and determines whether to calculate and update the controller by judging whether to meet the given triggering condition.
The advantages of the periodic event trigger mechanism can be analyzed from table 1:
1) compared with the traditional periodic sampling control, under different sampling periods, the system saves the calculation and updating times of the controller to different degrees, reduces the abrasion among parts to different degrees and prolongs the service life of the actuator. When the sampling period is smaller, the unnecessary updating times of the controller are more, and the communication and calculation resources saved by the periodic event trigger mechanism are more; with the increase of the sampling period, the unnecessary controller updating times are reduced, and the communication and calculation resources saved by the periodic event triggering mechanism are reduced.
2) Compared with a continuous event trigger mechanism, the periodic event trigger mechanism has the advantages that extra hardware is not needed to monitor the system state in real time, and the communication and computing resource saving degree is high; meanwhile, with the increase of the sampling period, the number of event triggers is less and less, and the control strategy shows the engineering application value.
Nothing in this specification is said to apply to the prior art.

Claims (8)

1. A lower limb exoskeleton sliding mode control method based on a periodic event trigger mechanism is characterized by comprising the following operation steps:
step 1: establishing a lower limb exoskeleton system dynamic model according to a Lagrange equation, and deducing a state space expression and a system comprehensive state vector expression;
step 2: acquiring lower limb movement data of a healthy human body by using a sensor, and acquiring an expected track of a lower limb exoskeleton joint through function fitting, specifically acquiring an angle expected track, an angular velocity expected track and an angular acceleration expected track; obtaining a system comprehensive state vector by combining the expected track, the actual operation angle and the angular speed, and calculating a system measurement error according to the system comprehensive state vector of the previous event triggering time and the current sampling time;
and step 3: presetting a threshold value and a sampling period of a measurement error, and designing a sliding mode controller based on a period event trigger mechanism for controlling a lower limb exoskeleton system according to the threshold value and the sampling period of the measurement error;
and 4, step 4: the Lyapunov theory is utilized to prove that the designed sliding mode controller based on the periodic event trigger mechanism can ensure the asymptotic stability of the lower limb exoskeleton system;
and 5: and (3) establishing a Matlab/Simulink simulation system under sliding mode control of the lower extremity exoskeleton system under a periodic event trigger mechanism for simulation, analyzing a simulation result and verifying the effectiveness of the method provided by the invention.
2. The method for controlling the sliding mode of the lower extremity exoskeleton of the system according to claim 1, wherein the dynamic equation of the lower extremity exoskeleton system in step 1 is as follows:
Figure FDA0002621013470000011
f (theta) < alpha >, < alpha > and,
Figure FDA0002621013470000012
G (theta) is respectively abbreviated as F, H, G, and the obtained product is obtained by arranging:
Figure FDA0002621013470000013
wherein θ ═ θ1,θ2]TIs a lower extremity exoskeleton joint angle vector, and θ1And theta2The angles of the hip joint and the knee joint respectively;
Figure FDA0002621013470000021
and
Figure FDA0002621013470000022
respectively representing the joint angular velocity and angular acceleration vectors of the lower limb exoskeleton; f (theta) belongs to R2×2A generalized inertia matrix;
Figure FDA0002621013470000023
is a matrix of centrifugal and coriolis forces; g (theta) ∈ R2Representing a gravity vector; τ ═ τ [ τ ]1,τ2]TRepresents a control moment vector, and1and τ2Respectively representing the control torque of the lower limb exoskeleton hip joint and the knee joint driver; tau ish＝[τh1,τh2]TRepresents the wearer joint moment vector, and τh1And τh2Respectively representing the control moment of the hip joint and the knee joint of the human body; d ═ F-1τhRepresenting a system interference vector;
according to the formula (2), the state space expression is obtained as follows:
Figure FDA0002621013470000024
the simplified state space expression is:
Figure FDA0002621013470000025
wherein,
Figure FDA0002621013470000026
represents a tracking error, and e1And e2Respectively tracking errors of the exoskeleton hip joint and the knee joint; thetadThe desired trajectory for the lower extremity exoskeleton joint angles,
Figure FDA0002621013470000027
the desired trajectory for the angular velocity is,
Figure FDA0002621013470000028
an expected trajectory for angular acceleration; vector quantity
Figure FDA0002621013470000029
In order to synthesize the state vector for the system,
Figure FDA00026210134700000210
3. the method for controlling the lower extremity exoskeleton sliding mode based on the periodic event triggering mechanism according to claim 1, wherein the specific process for acquiring the desired trajectory of the lower extremity exoskeleton joint in step 2 is as follows:
the angle expected track and the angular speed expected track of the lower extremity exoskeleton joint are thetad＝[θd1,θd2]T、
Figure FDA00026210134700000211
Having the formula:
Figure FDA00026210134700000212
measuring related data of a healthy human body in the walking process through an angular displacement sensor, and fitting the data into a fourth-order Fourier curve through a curveshaping tool box in Matlab to obtain a constant a in the formula (5)l,j、bl,jSo as to obtain an angle expected track and an angular velocity expected track of the lower extremity exoskeleton joint, and further obtain an angular acceleration expected track; a isl,0For the lower extremity exoskeleton angle desired value, omega, at the initial momentlIs a Fourier series frequency; by choosing an appropriate constant c0、c1、c2、c3> 0 such that thetad||≤c0，
Figure FDA0002621013470000031
At each sampling moment, calculating the comprehensive state variable of the system according to the actual running angle, the angular speed and the expected track of the lower limb exoskeleton
Figure FDA0002621013470000032
And combining the system comprehensive state variable eta (t) at the moment of triggering the last eventi) Obtaining the measurement error
Figure FDA0002621013470000033
4. The lower extremity exoskeleton sliding mode control method based on the periodic event trigger mechanism according to claim 1, wherein the sliding mode controller based on the periodic event trigger mechanism in step 3 is specifically realized in the following manner: presetting a threshold value and a sampling period of a measurement error, and designing a sliding mode control law; calculating a comprehensive state vector of the system at each sampling moment, calculating a measurement error, and defining the condition that the measurement error reaches or exceeds a preset measurement error threshold value as an event; when an event occurs, the sliding mode controller is triggered to calculate and update the control law, the zero-order retainer ZOH is used for keeping the control law until the next event triggering moment, and then the actuator is used for regulating and controlling the running state of the lower limb exoskeleton; the event is monitored through continuous periodic sampling, and when the event occurs, the sliding mode controller regulates and controls the lower limb exoskeleton system, so that the measurement error is smaller than a preset measurement error threshold value, namely the running state of the lower limb exoskeleton system tends to or reaches a preset ideal state.
5. The method for controlling the lower extremity exoskeleton sliding mode based on the periodic event trigger mechanism according to claim 1, wherein the design process of the sliding mode controller based on the periodic event trigger mechanism in step 3 is as follows:
designing a sliding mode surface based on a track tracking error as follows:
s＝Λe1+e2(6)
in the formula, lambda is ═ diag [ lambda ]1,λ2]，λ1,λ2＞0；
The Lyapunov function was designed as:
Figure FDA0002621013470000041
deriving V yields:
Figure FDA0002621013470000042
the sliding mode controller and the periodic event triggering conditions are designed as follows:
Figure FDA0002621013470000043
K＞0,K1＞d0+(1+)α (10)
Figure FDA0002621013470000044
Figure FDA0002621013470000045
wherein the time t ∈ [ t ]i,ti+1) And t isiRepresents the moment of occurrence of the ith event of the system, phi is a function of the vector eta; sign(s) ═ signs1,signs2]TRepresenting a symbolic function vector; h represents the sampling period of the system; measurement error
Figure FDA0002621013470000046
Where t e [ t ∈ [ [ t ]i,ti+1) (ii) a The constant satisfies 0 < 1 and the constant alpha > 0; constant beta is | | F-1Upper bound of |, LiFor a function phi in a set phiiLipschitz constant of, here
Figure FDA0002621013470000047
According to the Lipschitz condition, when eta + e, eta belongs to phiiTime of flight
Figure FDA0002621013470000048
For the system to be stable, the control gain K is set to any normal number, and the gain K is switched1＞d0+(1+)α，d0Is the upper bound of system disturbance, which is any normal number; at time t e [ t ∈i,ti+1) In that the sampling period h is less than
Figure FDA0002621013470000049
m＝[K+(λmax+λmin)(λmax+1)/λmin]w+d0+c1+c2+c3，λmin、λmaxRespectively the minimum and maximum eigenvalues of the matrix Λ, w is greater than or equal to norm | | | s (0) | | of the initial sliding mode surface;
substituting the control law formula (9) into the formula (8), when t is the same as [ t ]i,ti+1) Then, obtaining:
Figure FDA0002621013470000051
when η + e, η ∈ Φ, obtained by combining formula (14) and formula (15)iTime of flight
Figure FDA0002621013470000052
6. The method for controlling the lower extremity exoskeleton sliding mode based on the periodic event trigger mechanism according to claim 1, wherein the specific process of step 4 is as follows: the stability of the sliding mode controller based on the periodic event trigger mechanism, which is designed in the step 3, is verified by analyzing the stability problem of the system in different sampling periods, and the stability is specifically divided into the following conditions:
1) when the limit case sampling period h is equal to 0, the constant is equal to 0 and the gain K is switched1＞d0+ α, conditional (11) is equivalent to a continuous event triggered condition; firstly, the method of inversing the syndrome proves when t is an element of ti,ti+1) Time, eta + e, eta e phiiThe situation is always established; is obtained by definition
Figure FDA0002621013470000053
Let eta ∈ phiiAt t ∈ [ t ]i,ti+1) The time is not always true, and the existence time can be known due to the continuity of s
Figure FDA0002621013470000054
Satisfy the requirement of
Figure FDA0002621013470000055
And is
Figure FDA0002621013470000056
However, when
Figure FDA0002621013470000057
Time of flight
Figure FDA0002621013470000058
Still, it is possible, as can be seen by the trigger condition,
Figure FDA0002621013470000059
in combination with formula (14) to
Figure FDA00026210134700000510
Namely, it is
Figure FDA00026210134700000511
It contradicts assumptions; it is therefore concluded that,
Figure FDA00026210134700000512
and does not exist, i.e. at t e [ t ]i,ti+1) Time eta e phiiThe situation is always established; in combination with formula (16), yields:
Figure FDA00026210134700000513
from the above equation, the slip-form surface s is consistently bounded and limited
Figure FDA00026210134700000514
Is present;
integrating the two sides of the inequality (17) to obtain:
Figure FDA00026210134700000515
the above formula is combined with the Barbalt theorem to obtain
Figure FDA00026210134700000516
Namely, it is
Figure FDA00026210134700000517
The system is therefore asymptotically stable;
according to the definition, e can be obtained2＝-Λe1+ s, so the system can be written as:
Figure FDA0002621013470000061
considering the Lyapunov function
Figure FDA0002621013470000062
And deriving it to yield:
Figure FDA0002621013470000063
according to the consistency and the boundedness of s, the | | | s | ≦ s (0) | | | w is obtained by combining the formula (18):
Figure FDA0002621013470000064
according to the above formula, if | | | e1||＞w/λminThen, then
Figure FDA0002621013470000065
If true, further get | | | e1||≤w/λmin(ii) a According to the nature of the triangle inequality, | | e2||≤λmax||e1||+||s||≤λmaxw/λmin+w；
Combined triangle inequality pair
Figure FDA0002621013470000066
And (5) derivation to obtain:
Figure FDA0002621013470000067
2) when the sampling period h is greater than 0, the constant is greater than 0 and the gain K is switched1＞d0+ (1+) α; at the moment, the event can be monitored only at the sampling moment; so when t e [ t ]i,ti+1) Time inequality
Figure FDA0002621013470000068
Cannot be guaranteed to be established constantly; however, when the sampling period h is close to 0, when h is small enough, there is a constant
Figure FDA0002621013470000069
And is
Figure FDA00026210134700000610
So that
Figure FDA00026210134700000611
The method obtains the current t epsilon [ t ] by using a back-syndrome method in the same wayi,ti+1) Time, eta + e, eta e phiiIf this is always true, the equation (17) is obtained by combining the equation (16), and the system asymptotic stability is further obtained.
7. The method for controlling the lower extremity exoskeleton sliding mode based on the periodic event trigger mechanism according to claim 1, wherein the specific process of setting the sampling period is as follows: according to the process of analyzing the stability problem of the system in different sampling periods, t is the ∈ [ t ∈ [ [ t ]i,ti+1) There is a sufficiently small normal number h*H is less than or equal to h*Time inequality
Figure FDA0002621013470000071
Meets the requirements; according to the above description, if the error is measured
Figure FDA0002621013470000072
Satisfy inequality
Figure FDA0002621013470000073
The system asymptotically stabilizes; similar to the derivation of equation (22), further we can derive:
Figure FDA0002621013470000074
consider the following two cases:
1) if the event trigger condition (11) happens to be satisfied at the sampling time, the events are triggered synchronously and for t e [ t ∈ [ [ t ]i,ti+1)，
Figure FDA0002621013470000075
2) If the event trigger condition (11) is satisfied before the sample arrives, i.e.
Figure FDA0002621013470000076
When the conditional expression (11) is satisfied, the event is at ti+1＝ti+kih, triggering; for the
Figure FDA0002621013470000077
To differential isEquation (23) is integrated on both sides, yielding:
Figure FDA0002621013470000078
the arrangement (24) gives:
Figure FDA0002621013470000079
to ensure
Figure FDA00026210134700000710
Design parameters
Figure FDA00026210134700000711
When h is less than or equal to h*Xi (h)*)＜(1+)α/(βLi)。
8. The method for controlling the lower extremity exoskeleton sliding mode based on the periodic event trigger mechanism according to claim 1, wherein the Matlab/Simulink simulation system in the step 5 is composed of a system expected track, a periodic event trigger, a sliding mode controller and a lower extremity exoskeleton model, and the system expected track and an actual track of the lower extremity exoskeleton model changing along with time are combined to calculate a system measurement error; and inputting the measurement error into a periodic event trigger to generate a trigger time, and inputting the trigger time into a sliding mode controller to obtain a sliding mode control law and inputting the trigger time into a lower limb exoskeleton model for regulation and control to form closed-loop feedback.
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